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Zbl 0802.34021
Kannan, Rangachary; Nagle, R.Kent; Pothoven, Kenneth L.
Remarks on the existence of solutions of $x''+x+\arctan(x')=p(t)$; $x(0)=x(\pi)=0$. (English)
[J] Nonlinear Anal., Theory Methods Appl. 22, No.6, 793-796 (1994). ISSN 0362-546X

Of concern is the boundary value problem listed in the title of the paper, where $p$ is a continuous given function. The authors use the contraction mapping principle to prove an existence and uniqueness result when $\Vert p\Vert\sb \infty$ is sufficiently small. Other conditions and approaches for existence are also discussed.
[S.Aizicovici (Athens / Ohio)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34C25 Periodic solutions of ODE

Keywords: boundary value problem; contraction mapping principle; existence; uniqueness

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